A generalization of truncated M-fractional derivative and applications to fractional differential equations

In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]...

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Bibliographic Details
Published in:Applied mathematics and nonlinear sciences 2020-01, Vol.5 (1), p.171-188
Main Authors: İlhan, Esin, Kıymaz, İ. Onur
Format: Article
Language:English
Subjects:
26A33
33E20
34A08
alternative fractional derivative
conformable fractional derivative
M-series
Truncated M-fractional derivative
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Summary:In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.
ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2020.1.00016